Supplementary Information 1
Assessing ecosystem effects on the stock productivity of Antarctic Krill (Euphausia superba): An Integrated modeling perspective
Mardones, M; Jarvis Mason, E.T.; Pinones, A.; Santa Cruz, F.; Cárdenas, C.A
01 April, 2025
## [1] 16# dir01 <- here('s01') # agreggate data (no
# spatial diferences) dir1<-here('s1') # Data
# strata flishery dir2<-here('s2') # Same 9 with
# areas (SubStrata) as fleet. Dif size
# comoposition and dif CPUE and dif survey length
# and biomass data by strata dir3<-here('s3') #
# without S-R dir4<-here('s4') # dir5<-here('s5')
# # dir6<-here('s6') # dir7<-here('s7') # 2 set
# parametres EMM-2024/23 (Mardones)
# dir8<-here('s8') # s1 platoons dir9<-here('s9')
# # s1 w/ blocks
dir1.1 <- here("s1.1") # sin predador ni ambiental
dir1.2 <- here("s1.2") # s1.1 C/ predador
dir1.3 <- here("s1.3") # s1.1 solo env
dir1.4 <- here("s1.4") # s1.2 predator and env
Figs <- here("Figs") # SOVERVIEW
This study aims to evaluate the impact of ecosystem components—such as environmental variables and predator-prey interactions—on the productivity and key population dynamics of Euphausia superba in Subarea 48.1. By incorporating these factors into the assessment, we analyze how krill population variables respond to ecological variability, providing insights into their resilience and potential management implications.
Here, the reference model represents a baseline assessment of Euphausia superba population dynamics in Subarea 48.1, excluding environmental and ecological variables. This model assumes that krill productivity and population parameters are driven by intrinsic biological processes, such as growth, mortality, and recruitment and fishery impacts without accounting for external influences like environmental variability or predation pressure. By serving as a control scenario, this model provides a benchmark against which the impact of ecosystem components in productivity can be evaluated, allowing for a direct comparison of how environmental and ecological factors influence krill stock dynamics.
Statistical Model (SS3)
Stock Synthesis (v.3.30.21) is a widely used tool for assessing fish
and invertebrate populations, including Antarctic krill. SS3 is
implemented in C++ with estimation enabled through
automatic differentiation (ADMB) (Fournier et al. 2012; Methot and Wetzel 2013). In this
exercise, SS3 is configured as an integrated stock assessment model,
explicitly accounting for age and size structure while incorporating key
ecosystem drivers. The model simulates population processes such as
growth, maturity, fecundity, recruitment, movement, and mortality, while
also integrating environmental variability and predator-prey
relationships to refine estimates of population trends. The analysis of
model outputs is conducted using R, utilizing the r4ss and
ss3diags packages (Taylor 2019; Winker
et al. 2024). By leveraging a spatially implicit,
ecosystem-informed approach, this assessment provides a robust framework
for evaluating krill stock dynamics under changing environmental
conditions. These insights are crucial for informing sustainable
management strategies in the Antarctic Peninsula region, where krill
plays a foundational role in the marine food web.
Parameters
The following table summarizes the key parameters to conditioning the reference model, including biological, growth, and population dynamics factors.
| LO | HI | INIT | PHASE | |
|---|---|---|---|---|
| Natural Mortality | ||||
| Nat M | 0.20 | 1.00 | 0.270 | -3 |
| Growth | ||||
| Lmin | 0.00 | 5.00 | 3.400 | -2 |
| Lmax | 1.00 | 10.00 | 5.000 | -4 |
| VonBert K | 0.05 | 0.80 | 0.470 | -4 |
| CV young | 0.05 | 0.25 | 0.140 | -4 |
| CV old | 0.05 | 0.25 | 0.070 | -4 |
| relationship Length-Weigth | ||||
| Wt a | 0.00 | 3.00 | 0.000 | -3 |
| Wt b | 1.00 | 4.00 | 3.347 | -3 |
| Maturity | ||||
| L50% | 0.20 | 5.00 | 1.800 | -4 |
| Mat slope | -3.00 | 3.00 | -2.900 | -4 |
| S-R relation | ||||
| SR_LN(R0) | 3.00 | 30.00 | 23.000 | 1 |
| SR_BH_steep | 0.20 | 1.00 | 0.850 | -4 |
| SR_sigmaR | 0.00 | 2.00 | 1.200 | -4 |
| SR_regime | -5.00 | 5.00 | 0.000 | -4 |
| SR_autocorr | 0.00 | 0.00 | 0.000 | -99 |
| Catchability | ||||
| LnQ_base_FISHERYBS(1) | -25.00 | 25.00 | -5.722 | 1 |
| LnQ_base_FISHERYEI(2) | -25.00 | 25.00 | -5.722 | 1 |
| Selectivity | ||||
| SizeSel_P_1_FISHERYBS(1) | 0.01 | 8.00 | 2.000 | -3 |
| SizeSel_P_2_FISHERYBS(1) | 0.00 | 8.00 | 2.000 | -2 |
| SizeSel_P_1_FISHERYEI(2) | 0.01 | 8.00 | 3.500 | -3 |
| SizeSel_P_2_FISHERYEI(2) | 0.00 | 8.00 | 4.000 | -2 |
| SizeSel_P_1_FISHERYGS(3) | 0.01 | 8.00 | 2.000 | -3 |
| SizeSel_P_2_FISHERYGS(3) | 0.00 | 8.00 | 2.000 | 2 |
| SizeSel_P_1_FISHERYJOIN(4) | 0.01 | 8.00 | 3.500 | -3 |
| SizeSel_P_2_FISHERYJOIN(4) | 0.00 | 8.00 | 2.000 | -2 |
| SizeSel_P_1_FISHERYSSIW(5) | 0.01 | 8.00 | 3.500 | -3 |
| SizeSel_P_2_FISHERYSSIW(5) | 0.00 | 8.00 | 2.000 | -2 |
| SizeSel_P_1_SURVEYBS(6) | 1.00 | 7.00 | 2.000 | -2 |
| SizeSel_P_2_SURVEYBS(6) | 1.00 | 7.00 | 1.000 | -3 |
| SizeSel_P_1_SURVEYEI(7) | 1.00 | 7.00 | 3.000 | -2 |
| SizeSel_P_2_SURVEYEI(7) | 1.00 | 7.00 | 1.000 | -3 |
| SizeSel_P_1_SURVEYGS(8) | 1.00 | 7.00 | 2.000 | -2 |
| SizeSel_P_2_SURVEYGS(8) | 1.00 | 7.00 | 1.000 | -3 |
| SizeSel_P_1_SURVEYJOIN(9) | 1.00 | 7.00 | 3.000 | 2 |
| SizeSel_P_2_SURVEYJOIN(9) | 1.00 | 7.00 | 1.000 | 3 |
| SizeSel_P_1_SURVEYSSIW(10) | 1.00 | 7.00 | 2.000 | -2 |
| SizeSel_P_2_SURVEYSSIW(10) | 1.00 | 7.00 | 1.000 | -3 |
| SizeSel_P_1_PREDATOR(11) | 0.00 | 3.00 | 0.200 | 2 |
| SizeSel_P_2_PREDATOR(11) | 0.00 | 3.00 | 0.200 | 3 |
Source of data inpit
Scenarios
In Table 1 we have ten scenarios to test different option in modeling about main consideration in assessment of krill population.
| Scenario | Description |
|---|---|
| s1.1 | Spatial data without environmental and predator components |
| s1.2 | “s1.1” with predator components |
| s1.3 | “s1.1” with environmental variable |
| s1.4 | “s1.1” w/ both, predator fleet and environmental variable |
Run Models
Data used en both (spatial and No spatial models)
s1.1
and s1.4
RESULTS
Main Variables poulation in s1.1 scenario
Main Variables poulation in s1.2 scenario
Main Variables poulation in s1.3 scenario
Main Variables poulation in s1.4 scenario
Selectivity
Total biomass
Heatmap
hexagon
Diagnosis Base Model
A rigorous model diagnosis is essential to ensure the reliability and robustness of stock assessment models. The key steps for a good practice in model diagnosis include:
Convergence Check: The model must reach a final convergence criterion of 1.0e-04 to ensure numerical stability and reliable parameter estimation.
Residual Analysis: Both visual inspection and statistical metrics are used to evaluate model residuals, helping to detect patterns of bias or misfit.
Retrospective Analysis: The Mohn’s rho parameter is used to assess the consistency of model estimates when sequentially removing recent years of data, identifying potential overestimation or underestimation trends.
Likelihood Profile Analysis: This approach examines how the likelihood function behaves across a range of parameter values, providing insight into parameter uncertainty and model sensitivity.
This framework follows the recommendations outlined by Carvalho et al. (2021), aiming to enhance transparency and reproducibility in model evaluation.
Residual consistency
Residual analysis is a critical component of model diagnostics in stock assessments. It helps evaluate the fit of the model to observed data and detect potential biases or inconsistencies. This process is applied to both length composition data and abundance indices such as CPUE (Catch Per Unit Effort) and survey-derived estimates.
For length composition data, residuals represent the difference between observed and model-predicted length distributions. The standardized residuals are calculated as the difference between observed and expected proportions at each length bin. These residuals are plotted by year to identify systematic trends, biases, or inconsistencies in the data. Ideally, they should be randomly distributed around zero, indicating no systematic over- or underestimation.
For abundance indices such as CPUE and fishery-independent surveys, residuals are analyzed to assess model fit and potential sources of bias. Residuals are computed as the difference between observed index values and those predicted by the model, typically standardized by dividing by the standard error to facilitate comparison across years. These residuals are then plotted over time to evaluate trends. A shaded confidence region, like the green area in the provided plot, represents expected variability, with outliers highlighted in red or other distinct markers. Persistent positive or negative residuals may indicate systematic bias in the model or data collection process.
Statistical diagnostics are also performed to check for autocorrelation in residuals, which can indicate potential model misspecifications. When mean residual values are close to zero, the model fit is considered unbiased.
By integrating these residual analyses for both length and abundance indices, stock assessment models can be refined, improving their reliability and increasing confidence in the assessment results.
##
## Running Runs Test Diagnosics for Mean length
## Plotting Residual Runs Tests
##
## Runs Test stats by Mean length:## Index runs.p test sigma3.lo sigma3.hi type
## 1 FISHERYBS 0.218 Passed -0.1189633 0.1189633 len
## 2 FISHERYEI 0.013 Failed -0.2839347 0.2839347 len
## 3 FISHERYGS 0.912 Passed -0.1865475 0.1865475 len
## 4 FISHERYJOIN NA Excluded NA NA len
## 5 FISHERYSSIW 0.230 Passed -0.1176572 0.1176572 len
## 6 SURVEYBS 0.221 Passed -0.2220680 0.2220680 len
## 7 SURVEYEI 0.595 Passed -0.2119927 0.2119927 len
## 8 SURVEYGS 0.454 Passed -0.2928749 0.2928749 len
## 9 SURVEYJOIN 0.541 Passed -0.4156365 0.4156365 len##
## Running Runs Test Diagnosics for Mean length
## Plotting Residual Runs Tests
##
## Runs Test stats by Mean length:## Index runs.p test sigma3.lo sigma3.hi type
## 1 FISHERYBS 0.150 Passed -0.04986852 0.04986852 len
## 2 FISHERYEI 0.013 Failed -0.30357206 0.30357206 len
## 3 FISHERYGS 0.346 Passed -0.38742103 0.38742103 len
## 4 FISHERYJOIN NA Excluded NA NA len
## 5 FISHERYSSIW 0.230 Passed -0.14854188 0.14854188 len
## 6 SURVEYBS 0.001 Failed -0.29126384 0.29126384 len
## 7 SURVEYEI 0.627 Passed -0.22413735 0.22413735 len
## 8 SURVEYGS 0.409 Passed -0.35196215 0.35196215 len
## 9 SURVEYJOIN 0.500 Passed -0.44688062 0.44688062 len
## 10 PREDATOR 0.607 Passed -0.18346375 0.18346375 len##
## Running Runs Test Diagnosics for Mean length
## Plotting Residual Runs Tests
##
## Runs Test stats by Mean length:## Index runs.p test sigma3.lo sigma3.hi type
## 1 FISHERYBS 0.744 Passed -0.08525923 0.08525923 len
## 2 FISHERYEI 0.013 Failed -0.27984372 0.27984372 len
## 3 FISHERYGS 0.179 Passed -0.20160902 0.20160902 len
## 4 FISHERYJOIN NA Excluded NA NA len
## 5 FISHERYSSIW 0.230 Passed -0.12113187 0.12113187 len
## 6 SURVEYBS 0.631 Passed -0.22746036 0.22746036 len
## 7 SURVEYEI 0.786 Passed -0.18187931 0.18187931 len
## 8 SURVEYGS 0.136 Passed -0.29411566 0.29411566 len
## 9 SURVEYJOIN 0.500 Passed -0.41808588 0.41808588 len##
## Running Runs Test Diagnosics for Mean length
## Plotting Residual Runs Tests
##
## Runs Test stats by Mean length:## Index runs.p test sigma3.lo sigma3.hi type
## 1 FISHERYBS 0.500 Passed -0.04709602 0.04709602 len
## 2 FISHERYEI 0.013 Failed -0.27986404 0.27986404 len
## 3 FISHERYGS 0.013 Failed -0.26812009 0.26812009 len
## 4 FISHERYJOIN NA Excluded NA NA len
## 5 FISHERYSSIW 0.064 Passed -0.11843515 0.11843515 len
## 6 SURVEYBS 0.001 Failed -0.29845897 0.29845897 len
## 7 SURVEYEI 0.627 Passed -0.22182714 0.22182714 len
## 8 SURVEYGS 0.198 Passed -0.36195876 0.36195876 len
## 9 SURVEYJOIN 0.500 Passed -0.44265910 0.44265910 len
## 10 PREDATOR 0.607 Passed -0.26298700 0.26298700 lenResidual Analysis and RMSE
Residual analysis of mean length data is a fundamental diagnostic tool in stock assessments. It helps evaluate whether the model provides an unbiased fit to the observed data and detects potential biases over time. In this figure, mean length residuals are plotted across years, differentiated by data source, including fishery-dependent (FISHERY) and fishery-independent (SURVEY) datasets, as well as predator-related observations (PREDATOR). The residuals represent the deviation of observed mean length from model-predicted values, standardized to facilitate interpretation.
The black line represents a locally estimated scatterplot smoothing (Loess) curve, which provides a trend line to visualize systematic deviations over time. The presence of persistent positive or negative trends in the residuals may indicate biases in the growth model, selectivity assumptions, or misrepresentation of recruitment variability. The gray bars highlight periods where residual variability is particularly high, suggesting potential inconsistencies between observed and predicted size structures.
RMSE quantifies the overall deviation between observed and predicted values, providing an aggregate measure of model fit. Lower RMSE values indicate better agreement between observed and predicted data. In fisheries stock assessment (Hurtado-ferro et al. 2015), RMSE thresholds for acceptable model performance typically range between 10% and 30%, depending on the data quality and complexity of the population dynamics being modeled. Values exceeding this range suggest potential biases, requiring further investigation into the model structure, parameter estimation, or data sources.
By analyzing residual patterns and RMSE values, the model can be refined to improve the accuracy of mean length predictions, ultimately enhancing the reliability of stock assessment outcomes and management recommendations.
## Plotting JABBA residual plot##
## RMSE stats by Index:## indices RMSE.perc nobs
## 1 FISHERYBS 5.1 16
## 2 FISHERYEI 13.4 14
## 3 FISHERYGS 7.5 12
## 4 FISHERYJOIN 6.3 3
## 5 FISHERYSSIW 4.2 17
## 6 SURVEYBS 9.4 20
## 7 SURVEYEI 7.7 21
## 8 SURVEYGS 12.7 19
## 9 SURVEYJOIN 14.5 12
## 10 Combined 9.7 134## Plotting JABBA residual plot##
## RMSE stats by Index:## indices RMSE.perc nobs
## 1 FISHERYBS 2.4 16
## 2 FISHERYEI 12.6 14
## 3 FISHERYGS 19.0 12
## 4 FISHERYJOIN 9.6 3
## 5 FISHERYSSIW 4.8 17
## 6 SURVEYBS 30.6 20
## 7 SURVEYEI 15.6 21
## 8 SURVEYGS 18.2 19
## 9 SURVEYJOIN 13.0 12
## 10 PREDATOR 13.5 29
## 11 Combined 16.6 163## Plotting JABBA residual plot##
## RMSE stats by Index:## indices RMSE.perc nobs
## 1 FISHERYBS 4.9 16
## 2 FISHERYEI 13.9 14
## 3 FISHERYGS 9.4 12
## 4 FISHERYJOIN 7.3 3
## 5 FISHERYSSIW 4.4 17
## 6 SURVEYBS 15.0 20
## 7 SURVEYEI 7.6 21
## 8 SURVEYGS 11.9 19
## 9 SURVEYJOIN 14.2 12
## 10 Combined 10.7 134## Plotting JABBA residual plot
##
## RMSE stats by Index:## indices RMSE.perc nobs
## 1 FISHERYBS 1.6 16
## 2 FISHERYEI 12.4 14
## 3 FISHERYGS 18.3 12
## 4 FISHERYJOIN 8.1 3
## 5 FISHERYSSIW 3.9 17
## 6 SURVEYBS 30.4 20
## 7 SURVEYEI 15.3 21
## 8 SURVEYGS 18.3 19
## 9 SURVEYJOIN 12.6 12
## 10 PREDATOR 16.4 29
## 11 Combined 16.8 163## Plotting JABBA residual plot##
## RMSE stats by Index:## indices RMSE.perc nobs
## 1 FISHERYBS 60.7 20
## 2 FISHERYEI 52.9 22
## 3 FISHERYGS 66.1 16
## 4 FISHERYJOIN 52.7 8
## 5 FISHERYSSIW 52.7 23
## 6 SURVEYBS 95.7 21
## 7 SURVEYEI 79.9 18
## 8 SURVEYGS 115.2 20
## 9 SURVEYJOIN 148.8 7
## 10 SURVEYSSIW 99.7 2
## 11 Combined 81.3 157## Plotting JABBA residual plot##
## RMSE stats by Index:## indices RMSE.perc nobs
## 1 FISHERYBS 62.1 20
## 2 FISHERYEI 50.2 22
## 3 FISHERYGS 82.2 16
## 4 FISHERYJOIN 46.0 8
## 5 FISHERYSSIW 33.8 23
## 6 SURVEYBS 134.7 20
## 7 SURVEYEI 88.4 18
## 8 SURVEYGS 98.4 20
## 9 SURVEYJOIN 131.8 8
## 10 SURVEYSSIW 127.7 2
## 11 PREDATOR NaN 0
## 12 Combined 85.7 157## Plotting JABBA residual plot##
## RMSE stats by Index:## indices RMSE.perc nobs
## 1 FISHERYBS 63.7 20
## 2 FISHERYEI 50.0 22
## 3 FISHERYGS 70.3 16
## 4 FISHERYJOIN 46.2 8
## 5 FISHERYSSIW 50.1 23
## 6 SURVEYBS 121.9 20
## 7 SURVEYEI 94.3 18
## 8 SURVEYGS 119.7 21
## 9 SURVEYJOIN 123.7 7
## 10 SURVEYSSIW 131.0 2
## 11 Combined 87.0 157## Plotting JABBA residual plot
##
## RMSE stats by Index:## indices RMSE.perc nobs
## 1 FISHERYBS 62.5 20
## 2 FISHERYEI 48.2 22
## 3 FISHERYGS 81.0 16
## 4 FISHERYJOIN 42.1 8
## 5 FISHERYSSIW 32.8 23
## 6 SURVEYBS 127.5 20
## 7 SURVEYEI 91.5 18
## 8 SURVEYGS 112.8 21
## 9 SURVEYJOIN 129.3 8
## 10 SURVEYSSIW 132.7 2
## 11 PREDATOR NaN 0
## 12 Combined 86.6 158Comparision RMSE
## Model1.1 Model1.2 Model1.3 Model1.4
## Min. :0.5268 Min. :0.3375 Min. :0.4619 Min. :0.3279
## 1st Qu.:0.5480 1st Qu.:0.5314 1st Qu.:0.5347 1st Qu.:0.5176
## Median :0.7302 Median :0.8531 Median :0.8229 Median :0.8625
## Mean :0.8826 Mean :0.8969 Mean :0.9325 Mean :0.8845
## 3rd Qu.:0.9867 3rd Qu.:1.2493 3rd Qu.:1.2814 3rd Qu.:1.2519
## Max. :1.8820 Max. :1.5809 Max. :1.6408 Max. :1.5163
## Df Sum Sq Mean Sq F value Pr(>F)
## rep(1:4, each = nrow(dfrmse)) 1 0.001 0.00085 0.005 0.945
## Residuals 38 6.638 0.17469##
## Welch Two Sample t-test
##
## data: dfrmse$Model1.1 and dfrmse$Model1.2
## t = -0.07429, df = 17.971, p-value = 0.9416
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.4192226 0.3905904
## sample estimates:
## mean of x mean of y
## 0.8825568 0.8968729##
## Welch Two Sample t-test
##
## data: dfrmse$Model1.1 and dfrmse$Model1.3
## t = -0.25543, df = 17.998, p-value = 0.8013
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.4604222 0.3606026
## sample estimates:
## mean of x mean of y
## 0.8825568 0.9324666##
## Welch Two Sample t-test
##
## data: dfrmse$Model1.2 and dfrmse$Model1.3
## t = -0.18582, df = 17.985, p-value = 0.8547
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.4380513 0.3668639
## sample estimates:
## mean of x mean of y
## 0.8968729 0.9324666##
## Welch Two Sample t-test
##
## data: dfrmse$Model1.3 and dfrmse$Model1.4
## t = 0.25137, df = 17.978, p-value = 0.8044
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.3531612 0.4491482
## sample estimates:
## mean of x mean of y
## 0.9324666 0.8844731## Df Sum Sq Mean Sq F value Pr(>F)
## rep(1:4, each = nrow(dfrmse)) 1 0.001 0.00085 0.005 0.945
## Residuals 38 6.638 0.17469
This boxplot compares a summary of the Root Mean Square Error (RMSE)
across four different models (s1.1, s1.2, s1.3, and s1.4) used to
evaluate recruitment estimates of Antarctic krill. RMSE serves as an
indicator of model accuracy, with lower values representing better
predictive performance.
s1.1 exhibits the lowest median RMSE, suggesting it has the best overall fit among the four models. In contrast, Models 1.2, 1.3, and 1.4 show higher RMSE values, indicating comparatively lower predictive accuracy. The interquartile range (IQR) of these models is relatively similar, suggesting comparable variability in RMSE across models. Additionally, s1.1 has an outlier above 1.5 RMSE, which could indicate a case where the model’s predictions deviated significantly from observed values.
Overall, this analysis highlights that incorporating different environmental or predator-related variables in the models impacts their predictive ability. The differences in RMSE suggest that some models may overfit or underfit the recruitment patterns of krill, emphasizing the need to refine model selection based on ecological and statistical considerations.
Relationship Stock-Recruit
\[ R = \frac{aS}{1 + bS} \]
Where:
- \(S\) is the spawning stock
biomass.
- \(R\) is the predicted
recruitment.
- \(a\) is the maximum recruitment
capacity.
- \(b\) regulates density dependence
(higher values of \(b\) result in a
lower plateau).
The blue line will show the asymptotic curve that describes the relationship between spawning stock biomass and recruitment.
Retrospective Analysis in Model Evaluation
Retrospective analyses provide insights into the differences in estimation patterns (underestimation or overestimation) among the models evaluated. These analyses assess the consistency and reliability of stock assessment models by systematically removing the most recent years of data and comparing the resulting estimates with the full dataset.
In this study, we conducted a retrospective analysis to examine the sensitivity of our recruitment and spawning stock biomass (SSB) estimates to the inclusion or exclusion of recent data. By applying this approach to multiple models, we identified potential biases and evaluated the stability of the recruitment estimates over time.
The retrospective patterns were assessed by calculating the relative error between the predictions of truncated datasets and the full dataset. These differences allowed us to detect trends in model performance, such as systematic overestimation or underestimation of key population parameters. Understanding these deviations is crucial for improving the robustness of the stock assessment models and ensuring more reliable projections for fisheries management.
Hindcast Cross-Validation and Prediction Skill
The Hindcast Cross-Validation (HCxval) diagnostic in Stock Synthesis
is implemented using the model outputs generated by the
r4ss::SS_doRetro() function. This diagnostic evaluates the
predictive performance of the model by comparing hindcast predictions
with observed data.
To assess prediction skill, we employ the Mean Absolute Scaled Error (MASE) as a robust metric. MASE is calculated by scaling the mean absolute error of the model predictions relative to the mean absolute error of a naïve baseline prediction. Specifically, the MASE score is computed as follows:
- A MASE score greater than 1 indicates that the model’s average forecasts are less accurate than a random walk model.
- A MASE score equal to 1 suggests that the model’s accuracy is similar to that of a random walk.
- A MASE score less than 1 indicates that the model performs better than a random walk.
- A MASE score of 0.5, for example, indicates that the model’s forecasts are twice as accurate as the naïve baseline prediction, suggesting the model has predictive skill.
This approach provides a rigorous evaluation of model forecasting capabilities and helps identify improvements for model calibration.
Kobe (status)
another
| Model | Quant | Rho.type | Rho.peel | Rho.Rho | Rho.ForcastRho |
|---|---|---|---|---|---|
| s1.1 | SSB | SSB | 2019 | -0.2970246 | -0.2944080 |
| s1.1 | SSB | SSB | 2018 | -0.2707308 | -0.5103302 |
| s1.1 | SSB | SSB | 2017 | -0.1872940 | -0.3297243 |
| s1.1 | SSB | SSB | 2016 | -0.1779392 | -0.1957271 |
| s1.1 | SSB | SSB | Combined | -0.2332471 | -0.3325474 |
| s1.1 | F | F | 2019 | 1.1909249 | 2.5686552 |
| s1.1 | F | F | 2018 | 0.7828193 | 1.5773644 |
| s1.1 | F | F | 2017 | 0.8435982 | 1.0765231 |
| s1.1 | F | F | 2016 | 0.3245750 | 1.1174145 |
| s1.1 | F | F | Combined | 0.7854794 | 1.5849893 |
| s1.2 | SSB | SSB | 2019 | -0.0827150 | -0.1016893 |
| s1.2 | SSB | SSB | 2018 | -0.4893559 | -0.5608395 |
| s1.2 | SSB | SSB | 2017 | -0.7272409 | -0.7935804 |
| s1.2 | SSB | SSB | 2016 | -0.4875969 | -0.8027882 |
| s1.2 | SSB | SSB | Combined | -0.4467272 | -0.5647244 |
| s1.2 | F | F | 2019 | 1.0251379 | 3.4863606 |
| s1.2 | F | F | 2018 | 1.0700408 | 3.1240360 |
| s1.2 | F | F | 2017 | 3.5165245 | 3.4961678 |
| s1.2 | F | F | 2016 | 0.8270261 | 5.1191803 |
| s1.2 | F | F | Combined | 1.6096823 | 3.8064362 |
| s1.3 | SSB | SSB | 2019 | -0.2631174 | -0.3176714 |
| s1.3 | SSB | SSB | 2018 | -0.3709787 | -0.4678843 |
| s1.3 | SSB | SSB | 2017 | -0.3342903 | -0.5396513 |
| s1.3 | SSB | SSB | 2016 | -0.3209827 | -0.3946523 |
| s1.3 | SSB | SSB | Combined | -0.3223423 | -0.4299648 |
| s1.3 | F | F | 2019 | 1.1085776 | 2.9726497 |
| s1.3 | F | F | 2018 | 0.8449169 | 2.3280948 |
| s1.3 | F | F | 2017 | 1.3134959 | 2.0784872 |
| s1.3 | F | F | 2016 | 0.7604930 | 2.1222896 |
| s1.3 | F | F | Combined | 1.0068708 | 2.3753803 |
| s1.4 | SSB | SSB | 2019 | -0.1266622 | -0.2006111 |
| s1.4 | SSB | SSB | 2018 | -0.4523622 | -0.6020788 |
| s1.4 | SSB | SSB | 2017 | -0.6106873 | -0.8405322 |
| s1.4 | SSB | SSB | 2016 | -0.4535118 | -0.7243463 |
| s1.4 | SSB | SSB | Combined | -0.4108059 | -0.5918921 |
| s1.4 | F | F | 2019 | 0.8803373 | 3.3155514 |
| s1.4 | F | F | 2018 | 0.8286323 | 3.1905901 |
| s1.4 | F | F | 2017 | 3.6632985 | 6.7126908 |
| s1.4 | F | F | 2016 | 0.4471872 | 14.4300252 |
| s1.4 | F | F | Combined | 1.4548638 | 6.9122144 |
Likelihood tables
Likelihood Profile
SSplotProfile()
Convergence Criteria
The convergence criterion used for model calibration is set to a final threshold of 0.0001 (or equivalently 1.0e-04). This criterion defines the minimum acceptable difference between successive model iterations. Convergence is considered achieved when the absolute change in the objective function value or key parameters falls below this threshold. A smaller convergence value ensures that the model achieves a high degree of accuracy and stability in its final estimates, indicating that further iterations are unlikely to result in significant changes to the parameter estimates.
piner Plot
Outputs
Outputs Model s1.1
| Yr | Era | Seas | Bio_all | Bio_smry | SpawnBio | Recruit_0 | |
|---|---|---|---|---|---|---|---|
| 1254 | 1989 | VIRG | 1 | 2184230 | 2176360 | 3565180 | 107962000 |
| 1255 | 1990 | INIT | 1 | 1498570 | 1490900 | 2259200 | 105278000 |
| 1256 | 1991 | TIME | 1 | 1498570 | 1490900 | 2259200 | 105278000 |
| 1257 | 1992 | TIME | 1 | 1616910 | 1609190 | 2452620 | 105844000 |
| 1258 | 1993 | TIME | 1 | 1723130 | 1715370 | 2661750 | 106370000 |
| 1259 | 1994 | TIME | 1 | 1814140 | 1806360 | 2839670 | 106759000 |
| 1260 | 1995 | TIME | 1 | 1889790 | 1881980 | 2987350 | 107049000 |
| 1261 | 1996 | TIME | 1 | 1951400 | 1943580 | 3107870 | 107266000 |
| 1262 | 1997 | TIME | 1 | 2000910 | 1993080 | 3204890 | 107430000 |
| 1263 | 1998 | TIME | 1 | 2031670 | 2031470 | 3280300 | 2722690 |
| 1264 | 1999 | TIME | 1 | 1950370 | 1950080 | 3329570 | 3861330 |
| 1265 | 2000 | TIME | 1 | 1709860 | 1703160 | 3365450 | 91895800 |
| 1266 | 2001 | TIME | 1 | 1523110 | 1504210 | 2802010 | 259242000 |
| 1267 | 2002 | TIME | 1 | 1638890 | 1627610 | 2264810 | 154705000 |
| 1268 | 2003 | TIME | 1 | 1971710 | 1971470 | 2294470 | 3332310 |
| 1269 | 2004 | TIME | 1 | 2079960 | 2078730 | 3317380 | 16879800 |
| 1270 | 2005 | TIME | 1 | 1916790 | 1913490 | 3747190 | 45270000 |
| 1271 | 2006 | TIME | 1 | 1724010 | 1708750 | 3238060 | 209287000 |
| 1272 | 2007 | TIME | 1 | 1640040 | 1631050 | 2612060 | 123361000 |
| 1273 | 2008 | TIME | 1 | 1833350 | 1832360 | 2343170 | 13566800 |
| 1274 | 2009 | TIME | 1 | 1869200 | 1864810 | 3037610 | 60221700 |
| 1275 | 2010 | TIME | 1 | 1731220 | 1719710 | 3226670 | 157914000 |
| 1276 | 2011 | TIME | 1 | 1606630 | 1586690 | 2567950 | 273609000 |
| 1277 | 2012 | TIME | 1 | 1905570 | 1872960 | 2385900 | 447447000 |
| 1278 | 2013 | TIME | 1 | 2520170 | 2519760 | 2744410 | 5517500 |
| 1279 | 2014 | TIME | 1 | 2918840 | 2914270 | 3602640 | 62737200 |
| 1280 | 2015 | TIME | 1 | 2758580 | 2740280 | 5255400 | 251086000 |
| 1281 | 2016 | TIME | 1 | 2672990 | 2619030 | 4425950 | 740188000 |
| 1282 | 2017 | TIME | 1 | 3269820 | 3269180 | 3819450 | 8874990 |
| 1283 | 2018 | TIME | 1 | 4057150 | 3997160 | 4289280 | 823040000 |
| 1284 | 2019 | TIME | 1 | 4780510 | 4672090 | 7517290 | 1487330000 |
| 1285 | 2020 | TIME | 1 | 6934500 | 6933840 | 6701380 | 8978140 |
| 1286 | 2021 | FORE | 1 | 8884260 | 8876160 | 10056300 | 111127000 |
| 1287 | 2022 | FORE | 1 | 8472730 | 8464580 | 16411100 | 111824000 |
| 1288 | 2023 | FORE | 1 | 7532870 | 7524730 | 14262700 | 111657000 |
| 1289 | 2024 | FORE | 1 | 6398190 | 6390070 | 11986300 | 111416000 |
| 1290 | 2025 | FORE | 1 | 5398930 | 5390840 | 9988720 | 111115000 |
Outputs Model s1.2
| Yr | Era | Seas | Bio_all | Bio_smry | SpawnBio | Recruit_0 | |
|---|---|---|---|---|---|---|---|
| 1354 | 1989 | VIRG | 1 | 2299170 | 2268860 | 2213450 | 415800000 |
| 1355 | 1990 | INIT | 1 | 2140700 | 2110590 | 1919210 | 413006000 |
| 1356 | 1991 | TIME | 1 | 2140700 | 2110590 | 1919210 | 413006000 |
| 1357 | 1992 | TIME | 1 | 2210510 | 2180300 | 2052100 | 414362000 |
| 1358 | 1993 | TIME | 1 | 2249080 | 2218830 | 2126300 | 415049000 |
| 1359 | 1994 | TIME | 1 | 2270970 | 2240690 | 2163880 | 415380000 |
| 1360 | 1995 | TIME | 1 | 2283380 | 2253090 | 2185490 | 415565000 |
| 1361 | 1996 | TIME | 1 | 2290340 | 2260040 | 2197820 | 415669000 |
| 1362 | 1997 | TIME | 1 | 2294230 | 2263930 | 2204700 | 415727000 |
| 1363 | 1998 | TIME | 1 | 2266810 | 2265650 | 2207770 | 15962500 |
| 1364 | 1999 | TIME | 1 | 1867210 | 1863690 | 2202490 | 48340700 |
| 1365 | 2000 | TIME | 1 | 1196690 | 1191800 | 2199340 | 67016200 |
| 1366 | 2001 | TIME | 1 | 828069 | 768871 | 1232060 | 812129000 |
| 1367 | 2002 | TIME | 1 | 1347830 | 1298870 | 737765 | 671607000 |
| 1368 | 2003 | TIME | 1 | 2369680 | 2367790 | 534842 | 25993000 |
| 1369 | 2004 | TIME | 1 | 2358800 | 2347400 | 2222130 | 156448000 |
| 1370 | 2005 | TIME | 1 | 1692350 | 1681210 | 2907030 | 152806000 |
| 1371 | 2006 | TIME | 1 | 1334460 | 1282450 | 1706020 | 713509000 |
| 1372 | 2007 | TIME | 1 | 1587260 | 1564820 | 1167630 | 307877000 |
| 1373 | 2008 | TIME | 1 | 2058080 | 2050430 | 968864 | 104953000 |
| 1374 | 2009 | TIME | 1 | 1799590 | 1784940 | 2225020 | 200938000 |
| 1375 | 2010 | TIME | 1 | 1401810 | 1386880 | 1981840 | 204876000 |
| 1376 | 2011 | TIME | 1 | 1141310 | 1130440 | 1172540 | 149095000 |
| 1377 | 2012 | TIME | 1 | 1076390 | 1042010 | 1058820 | 471730000 |
| 1378 | 2013 | TIME | 1 | 1258030 | 1225100 | 995034 | 451783000 |
| 1379 | 2014 | TIME | 1 | 1685050 | 1599720 | 774750 | 1170600000 |
| 1380 | 2015 | TIME | 1 | 2619570 | 2612840 | 1328470 | 92363200 |
| 1381 | 2016 | TIME | 1 | 2961350 | 2947640 | 1691030 | 188112000 |
| 1382 | 2017 | TIME | 1 | 2137730 | 2126280 | 3483620 | 157048000 |
| 1383 | 2018 | TIME | 1 | 1632790 | 1493160 | 2050430 | 1915550000 |
| 1384 | 2019 | TIME | 1 | 3002460 | 2903520 | 1450160 | 1357410000 |
| 1385 | 2020 | TIME | 1 | 5247580 | 5235720 | 1111080 | 162708000 |
| 1386 | 2021 | FORE | 1 | 5161170 | 5130090 | 5069530 | 426398000 |
| 1387 | 2022 | FORE | 1 | 3655000 | 3623850 | 5768290 | 427421000 |
| 1388 | 2023 | FORE | 1 | 2833070 | 2802300 | 3345400 | 422101000 |
| 1389 | 2024 | FORE | 1 | 2415010 | 2384550 | 2502690 | 417931000 |
| 1390 | 2025 | FORE | 1 | 2214670 | 2184410 | 2127620 | 415061000 |
Outputs Model s1.3
| Yr | Era | Seas | Bio_all | Bio_smry | SpawnBio | Recruit_0 | |
|---|---|---|---|---|---|---|---|
| 1305 | 1989 | VIRG | 1 | 1354540 | 1349660 | 2210920 | 66952200 |
| 1306 | 1990 | INIT | 1 | 925937 | 921186 | 1367470 | 65178600 |
| 1307 | 1991 | TIME | 1 | 925937 | 921186 | 1367470 | 65178600 |
| 1308 | 1992 | TIME | 1 | 1012370 | 1007590 | 1539740 | 65688900 |
| 1309 | 1993 | TIME | 1 | 1082790 | 1077970 | 1679460 | 66030400 |
| 1310 | 1994 | TIME | 1 | 1139590 | 1134760 | 1789740 | 66264200 |
| 1311 | 1995 | TIME | 1 | 1184920 | 1180070 | 1878070 | 66432800 |
| 1312 | 1996 | TIME | 1 | 1220820 | 1215970 | 1948280 | 66556400 |
| 1313 | 1997 | TIME | 1 | 1249200 | 1244350 | 2003870 | 66648400 |
| 1314 | 1998 | TIME | 1 | 1266420 | 1266130 | 2046680 | 3933970 |
| 1315 | 1999 | TIME | 1 | 1216010 | 1215500 | 2071380 | 7024060 |
| 1316 | 2000 | TIME | 1 | 1072540 | 1067770 | 2089420 | 65411200 |
| 1317 | 2001 | TIME | 1 | 972011 | 956267 | 1743630 | 215989000 |
| 1318 | 2002 | TIME | 1 | 1109210 | 1100090 | 1431580 | 125160000 |
| 1319 | 2003 | TIME | 1 | 1429620 | 1429580 | 1495100 | 561097 |
| 1320 | 2004 | TIME | 1 | 1554480 | 1552980 | 2429710 | 20540100 |
| 1321 | 2005 | TIME | 1 | 1457100 | 1454260 | 2840910 | 39008600 |
| 1322 | 2006 | TIME | 1 | 1336990 | 1324330 | 2463950 | 173714000 |
| 1323 | 2007 | TIME | 1 | 1281790 | 1274680 | 2002810 | 97556700 |
| 1324 | 2008 | TIME | 1 | 1457730 | 1456870 | 1826580 | 11786600 |
| 1325 | 2009 | TIME | 1 | 1495420 | 1492040 | 2433300 | 46468300 |
| 1326 | 2010 | TIME | 1 | 1380600 | 1374330 | 2577450 | 86071200 |
| 1327 | 2011 | TIME | 1 | 1216340 | 1201580 | 2007830 | 202457000 |
| 1328 | 2012 | TIME | 1 | 1370300 | 1353670 | 1857780 | 228170000 |
| 1329 | 2013 | TIME | 1 | 1695430 | 1695250 | 1914900 | 2452510 |
| 1330 | 2014 | TIME | 1 | 1790520 | 1786460 | 2457000 | 55652700 |
| 1331 | 2015 | TIME | 1 | 1629480 | 1613420 | 3067990 | 220458000 |
| 1332 | 2016 | TIME | 1 | 1591680 | 1567250 | 2434430 | 335175000 |
| 1333 | 2017 | TIME | 1 | 1924560 | 1917300 | 2100330 | 99619900 |
| 1334 | 2018 | TIME | 1 | 2324930 | 2262040 | 2686920 | 862770000 |
| 1335 | 2019 | TIME | 1 | 3241680 | 3138230 | 3990880 | 1419210000 |
| 1336 | 2020 | TIME | 1 | 5615900 | 5614770 | 4015250 | 15552100 |
| 1337 | 2021 | FORE | 1 | 7713090 | 7708050 | 8063680 | 69167000 |
| 1338 | 2022 | FORE | 1 | 7512020 | 7506950 | 14559700 | 69554800 |
| 1339 | 2023 | FORE | 1 | 6671280 | 6666210 | 12838900 | 69490000 |
| 1340 | 2024 | FORE | 1 | 5619480 | 5614420 | 10736700 | 69382900 |
| 1341 | 2025 | FORE | 1 | 4656920 | 4651870 | 8812160 | 69240500 |
Outputs Model s1.4
| Yr | Era | Seas | Bio_all | Bio_smry | SpawnBio | Recruit_0 | |
|---|---|---|---|---|---|---|---|
| 1305 | 1989 | VIRG | 1 | 1354540 | 1349660 | 2210920 | 66952200 |
| 1306 | 1990 | INIT | 1 | 925937 | 921186 | 1367470 | 65178600 |
| 1307 | 1991 | TIME | 1 | 925937 | 921186 | 1367470 | 65178600 |
| 1308 | 1992 | TIME | 1 | 1012370 | 1007590 | 1539740 | 65688900 |
| 1309 | 1993 | TIME | 1 | 1082790 | 1077970 | 1679460 | 66030400 |
| 1310 | 1994 | TIME | 1 | 1139590 | 1134760 | 1789740 | 66264200 |
| 1311 | 1995 | TIME | 1 | 1184920 | 1180070 | 1878070 | 66432800 |
| 1312 | 1996 | TIME | 1 | 1220820 | 1215970 | 1948280 | 66556400 |
| 1313 | 1997 | TIME | 1 | 1249200 | 1244350 | 2003870 | 66648400 |
| 1314 | 1998 | TIME | 1 | 1266420 | 1266130 | 2046680 | 3933970 |
| 1315 | 1999 | TIME | 1 | 1216010 | 1215500 | 2071380 | 7024060 |
| 1316 | 2000 | TIME | 1 | 1072540 | 1067770 | 2089420 | 65411200 |
| 1317 | 2001 | TIME | 1 | 972011 | 956267 | 1743630 | 215989000 |
| 1318 | 2002 | TIME | 1 | 1109210 | 1100090 | 1431580 | 125160000 |
| 1319 | 2003 | TIME | 1 | 1429620 | 1429580 | 1495100 | 561097 |
| 1320 | 2004 | TIME | 1 | 1554480 | 1552980 | 2429710 | 20540100 |
| 1321 | 2005 | TIME | 1 | 1457100 | 1454260 | 2840910 | 39008600 |
| 1322 | 2006 | TIME | 1 | 1336990 | 1324330 | 2463950 | 173714000 |
| 1323 | 2007 | TIME | 1 | 1281790 | 1274680 | 2002810 | 97556700 |
| 1324 | 2008 | TIME | 1 | 1457730 | 1456870 | 1826580 | 11786600 |
| 1325 | 2009 | TIME | 1 | 1495420 | 1492040 | 2433300 | 46468300 |
| 1326 | 2010 | TIME | 1 | 1380600 | 1374330 | 2577450 | 86071200 |
| 1327 | 2011 | TIME | 1 | 1216340 | 1201580 | 2007830 | 202457000 |
| 1328 | 2012 | TIME | 1 | 1370300 | 1353670 | 1857780 | 228170000 |
| 1329 | 2013 | TIME | 1 | 1695430 | 1695250 | 1914900 | 2452510 |
| 1330 | 2014 | TIME | 1 | 1790520 | 1786460 | 2457000 | 55652700 |
| 1331 | 2015 | TIME | 1 | 1629480 | 1613420 | 3067990 | 220458000 |
| 1332 | 2016 | TIME | 1 | 1591680 | 1567250 | 2434430 | 335175000 |
| 1333 | 2017 | TIME | 1 | 1924560 | 1917300 | 2100330 | 99619900 |
| 1334 | 2018 | TIME | 1 | 2324930 | 2262040 | 2686920 | 862770000 |
| 1335 | 2019 | TIME | 1 | 3241680 | 3138230 | 3990880 | 1419210000 |
| 1336 | 2020 | TIME | 1 | 5615900 | 5614770 | 4015250 | 15552100 |
| 1337 | 2021 | FORE | 1 | 7713090 | 7708050 | 8063680 | 69167000 |
| 1338 | 2022 | FORE | 1 | 7512020 | 7506950 | 14559700 | 69554800 |
| 1339 | 2023 | FORE | 1 | 6671280 | 6666210 | 12838900 | 69490000 |
| 1340 | 2024 | FORE | 1 | 5619480 | 5614420 | 10736700 | 69382900 |
| 1341 | 2025 | FORE | 1 | 4656920 | 4651870 | 8812160 | 69240500 |
Comparison
Comparison outputs betwwen scenarios
Comparison between select models
Ref Model: No Env-Predator and
S1.1 w/ Env and Predator data
Comparsion in sd long term time series
Autocorrelation in Recruit
To evaluate the temporal correlation structure of krill recruitment under different model configurations, we performed an Autocorrelation Function (ACF) analysis. The ACF measures the correlation between observations at different time lags, helping to assess whether recruitment estimates exhibit persistence or randomness across time.
The analysis was conducted on recruitment estimates derived from four model scenarios:
A reference model without environmental or predator influences (Ref Model: No Env-Predator). A model incorporating predator data (S1.1 w/ Predator data). A model incorporating environmental data (S1.1 w/ Env data). A model incorporating both environmental and predator data (S1.1 w/ Env and Predator data). Each model’s residuals were extracted, and the autocorrelation function (ACF) was computed for a time lag range of up to 15 years. The dashed blue lines in the plots represent the 95% confidence intervals, indicating the threshold beyond which correlation values are statistically significant. If autocorrelation values remain within this range, it suggests that the recruitment estimates behave as a random process with no significant dependence on past values. Conversely, autocorrelation values exceeding these bounds indicate recruitment persistence or cyclic patterns.
The ACF plots indicate that the reference model (without environmental or predator data) exhibits weak but noticeable positive autocorrelation at certain lags, suggesting some degree of recruitment dependence over time. However, this autocorrelation does not appear strong or systematic.
The model incorporating only predator data shows a slight reduction in autocorrelation magnitude, suggesting that predator-driven recruitment variability may have captured part of the temporal structure in the data.
The model with only environmental data exhibits a further reduction in autocorrelation, implying that environmental variability explains a larger portion of recruitment trends than predator effects alone.
Finally, the model that includes both environmental and predator data presents the lowest autocorrelation values, with nearly all bars remaining within the confidence bounds. This suggests that incorporating both factors provides the most effective explanation of recruitment fluctuations, reducing unexplained temporal structure.
Overall, these results indicate that recruitment variability is at least partially driven by environmental and predator influences, and models integrating these factors provide more robust and independent recruitment estimates, minimizing systematic dependencies over time.
Recruit deviation
Platoons analisis
### AKL
In a catch-at-length model like krill assessment the AKL matrix is modelled trought parametrization process
Representation of ALK Matrix to krill in 48.1